But Órfhlaith Begley does go to Westminster, and she has an access badge for the Houses of Parliament, and she flies over there and works in her office in the parliament buildings and answers her @parliament.co.uk emails and asks her staffers (paid for by the parliament) to respond to letters on paper headed Órfhlaith Begley MP. All the work of an MP except the most performative part.
She just doesn't go into the room which is called the House of Commons and try to speak or vote there, because the armed guards at the door won't let in anyone who doesn't swear allegiance to the King. If swearing allegiance to the King was a requirement to use the email system, then she wouldn't do that either.
Fascinating, I didn't know that they actually physically travel to Westminster. That does seem like quite a trip given they could work from home. I'm also not sure how effective you can be in this way, but of course it's really up to her constituents not me whether they feel adequately represented.
I think it's parliament.uk rather than parliament.co.uk by the way.